On our Amsterdam cruise, we only tendered in Sitka. But it might vary depending on how crowded the other ports are when the ship arrives. No big deal. If you have a shore excursion booked with the line or are in a suite, you have priority getting off. Otherwise if you wait until the initial rush is finished, there really isn't a long wait at any time to get off and on. If you are gung ho to get off early and don't fit into one of the other categories, you'll get a number and have a little wait -- not too bad.
They will announce a tendering procedure. Every line and ship is diffrent. The earlier you arrive to the designated tender ticket place to get your ticket, the earlier you get off, your ENTIRE group that is leaving the ship with you must be with you to obtain tender tickets. They then escort each tender group to the tenders when it is your turn. It's a very simple process.
Tendering is determined by how many ships are in port, who submitted the itinerary 1st to the harbormaster, how large is the ship and how it will fit into the docking berths.
Usually Princess and HAL have 1st dibs, because they have been in Alaska the longest
HAL can use its own lifeboat/tenders to move people ashore. Surprisingly roomy and comfortable.
Suite dwellers get preferential treatment going and coming.
Others, at least on the cruise I was last on, went to the theater, got a ticket and took a seat until your number was called. Most waited patiently, some *****ed and moaned. Once the initial surge was taken care of, you would be told to go directly to the tender landing, otherwise known as the hatch at the waterline where you leap into the boat.